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Bits, Data types, and Operations: Chapter 2

1. Bits, Data types, and Operations: Chapter 2. COMP 2610. Dr. James Money COMP 2610. Floating Point Data Type. Most ISAs have a data type called float , which is 32 bits arranged as follows 1 bit for sign 8 bits for range of exponent 23 bits for the precision or fraction

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Bits, Data types, and Operations: Chapter 2

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  1. 1 Bits, Data types, and Operations: Chapter 2 COMP 2610 Dr. James Money COMP 2610

  2. Floating Point Data Type • Most ISAs have a data type called float, which is 32 bits arranged as follows • 1 bit for sign • 8 bits for range of exponent • 23 bits for the precision or fraction • This is called the IEEE Standard for Floating Point Arithmetic

  3. Floating Point Data Type

  4. Floating Point Data Type • Recall the bits in the fractional part are of the form 1.b-1b-2…b-j • The corresponding decimal number is 1x20 + b-1x2-1+b-2x2-2+… + b-j 2-j

  5. Floating Point Data Type • If the exponent=00000000, then we can represent tiny numbers. • In this case, we assume the leading digit is zero and not 1 and exp=-126. That is, it is of the form -1s 0.fraction x 2-126

  6. Floating Point Data Type • Consider the floating point value 0 00000000 0000100000000000000000 • This is + 2-5 x 2-126 = 2-131

  7. Floating Point Data Type • Interpret the floating point values • 0 11111110 1111111111111111111111 • 1 00001101 0111000000000000000000 • 1 00000000 0000000000001000000000

  8. ASCII Codes • Another standard of representation is one for transferring character codes • This is an eight bit code referred to ASCII • ASCII stands for American Standard Code for Information Exchange • It simplifies the interface between I/O devices among companies

  9. ASCII Codes • Each key on a keyboard is identified by a unique ASCII code • The digit 3 is (00110011)2 = (41)10, digit 3 is (00110010)2 = (40)10 • The letter ‘e’ is (01100101)2 and carriage return is (00001101)2

  10. ASCII Codes • The list of codes are at the back of the book for all 256 ASCII codes • Some codes are associate with multiple keys, such as ‘e’ and ‘E’

  11. Hexadecimal Notation • One form that is common for reading values on the computer is called hexadecimal notation • Hexadecimal notation is the base 16 representation of the number

  12. Hexadecimal Notation • We use 0-9 for the same numbers in hexadecimal • What about 10-15? • We use the letters A-F

  13. Hexadecimal Notation • A – 10 • B – 11 • C – 12 • D – 13 • E – 14 • F - 15

  14. Hexadecimal Notation • Consider the binary string 0011110101101110 • This can be broken into groups of 4 bits: 0011 1101 0110 1110 • Now, recall that the range of 4 bits is 0 -15, just like hexadecimal notation

  15. Hexadecimal Notation • Hence, the numbers represent • We typically prefix this by x or 0x to indicate hexadecimal form • So our binary number is 0x3D6E

  16. Hexadecimal Notation • What is the number 0x5A6C in binary form? • Thus, (5A6C)16 = (0101 1010 0110 1100)2

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